1. Key Laboratory of Urban Underground Engineering of the Education Ministry, Beijing Jiaotong University, Beijing 100044, China 2. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
This study aims to investigate hydrofracturing in double-layered soil through theoretical and experimental analysis, as multilayered soils where the difference in mechanical properties exists are generally encountered in practical engineering. First, an analytical solution for fracturing pressure in two different concentric regions of soil was presented based on the cavity expansion theory. Then, several triaxial hydraulic fracturing tests were carried out to validate the analytical solution. The comparison between the experimental and analytical results indicates the remarkable accuracy of the derived formula, and the following conclusions were also obtained. First, there is a linear relationship between the fracturing pressure and confining pressure in concentric double-layered cohesive soil. Second, when the internal-layer soil is softer than the external-layer soil, the presence of internal soil on the fracturing pressure approximately brings the weakening effect, and the greater strength distinction between the two layers, the greater the weakening effect. Third, when the internal-layer soil is harder than the external-layer soil, the existence of the internal-layer soil has a strengthening effect on the fracturing pressure regardless of the proportion of internal-layer soil. Moreover, the influence of strength distinction between the two layers on the fracturing pressure is significant when the proportion of internal-layer soil is less than half, while it’s limited when the proportion is more than half. The proposed solution is potentially useful for geotechnical problems involving aspects of cohesive soil layering in a composite formation.
S Wu, T Li, H Ge, X Wang, N Li, Y Zou. Shear-tensile fractures in hydraulic fracturing network of layered shale. Journal of Petroleum Science Engineering, 2019, 183 : 106428– https://doi.org/10.1016/j.petrol.2019.106428
2
P Wang, X Mao, J Lin, C Du. Study of the borehole hydraulic fracturing and the principle of gas seepage in the coal seam. Procedia Earth and Planetary Science, 2009, 1( 1): 1561– 1573 https://doi.org/10.1016/j.proeps.2009.09.241
3
A Jenabidehkordi. Computational methods for fracture in rock: A review and recent advances. Frontiers of Structural and Civil Engineering, 2019, 13( 2): 273– 287 https://doi.org/10.1007/s11709-018-0459-5
4
Gottardi G, Cavallari L, Marchi M. Soil fracturing of soft silty clays for the reinforcement of a bell tower foundation. In: Proceedings of the 2nd International Workshop on Geotechnics of Soft Soils. Glasgow: CRC Press, 2008
5
J G Zhu, E Ji, Y Wen, H Zhang. Elastic-plastic solution and experimental study on critical water pressure inducing hydraulic fracturing in soil. Journal of Central South University, 2015, 22( 11): 4347– 4354 https://doi.org/10.1007/s11771-015-2983-y
6
Yuan D J, Huang Q F, Wang Y. Risk analysis and countermeasures of Nanjing Yangtze River tunnel during large diameter slurry shield tunneling. In: Proceedings of 2009 International Symposium on Risk Control and Management of Design, Construction and Operation in Underground Engineering. Dalian, 2009, 190−193
7
D Jin, Z Zhang, D Yuan. Effect of dynamic cutterhead on face stability in EPB shield tunneling. Tunnelling and Underground Space Technology, 2021, 110 : 103827– https://doi.org/10.1016/j.tust.2021.103827
8
D Jin, D Yuan, X Li, W Su. Probabilistic analysis of the disc cutter failure during TBM tunneling in hard rock. Tunnelling and Underground Space Technology, 2021, 109 : 103744– https://doi.org/10.1016/j.tust.2020.103744
9
Decker R A, Clemence S P. Laboratory study of hydraulic fracturing in clay. In: Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering. Stockholm: A.A. Balkema, 1981, 573–575
10
S Zhou, X Zhuang, T Rabczuk. Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Computer Methods in Applied Mechanics and Engineering, 2019, 355 : 729– 752 https://doi.org/10.1016/j.cma.2019.06.021
11
S Zhou, X Zhuang, T Rabczuk. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240 : 189– 203 https://doi.org/10.1016/j.enggeo.2018.04.008
12
A K Panah, E Yanagisawa. Laboratory studies on hydraulic fracturing criteria in soil. Soil and Foundation, 1989, 29( 4): 14– 22 https://doi.org/10.3208/sandf1972.29.4_14
13
M C Alfaro, R C K Wong. Laboratory studies on fracturing of low-permeability soils. Canadian Geotechnical Journal, 2001, 38( 2): 303– 315 https://doi.org/10.1139/t00-096
14
K Soga, S K A Au, M R Jafari, M D Bolton. Laboratory investigation of multiple grout injections into clay. Geotechnique, 2004, 54( 2): 81– 90 https://doi.org/10.1680/geot.2004.54.2.81
15
M Chang, R C Huang. Observations of hydraulic fracturing in soils through field testing and numerical simulations. Canadian Geotechnical Journal, 2016, 53( 2): 343– 359 https://doi.org/10.1139/cgj-2015-0193
16
E Yanagisawa, A K Panah. Two dimensional study of hydraulic fracturing criteria in cohesive soils. Soil and Foundation, 1994, 34( 1): 1– 9 https://doi.org/10.3208/sandf1972.34.1
17
P Q Mo, A M Marshall, H S Yu. Elastic-plastic solutions for expanding cavities embedded in two different cohesive-frictional materials. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38( 9): 961– 977 https://doi.org/10.1002/nag.2288
18
P Q Mo, H S Yu. Undrained cavity expansion analysis with a unified state parameter model for clay and sand. Geotechnique, 2017, 67( 6): 503– 515 https://doi.org/10.1680/jgeot.15.P.261
19
T Chen, T Pang, Y Zhao, D Zhang, Q Fang. Numerical simulation of slurry fracturing during shield tunnelling. Tunnelling and Underground Space Technology, 2018, 74 : 153– 166 https://doi.org/10.1016/j.tust.2018.01.021
20
B He. Hydromechanical model for hydraulic fractures using XFEM. Frontiers of Structural and Civil Engineering, 2019, 13( 1): 240– 249 https://doi.org/10.1007/s11709-018-0490-6
21
W Fang, J Wu, T Yu, T T Nguyen, T Q Bui. Simulation of cohesive crack growth by a variable-node XFEM. Frontiers of Structural and Civil Engineering, 2020, 14( 1): 215– 228 https://doi.org/10.1007/s11709-019-0595-6
22
S Zhou, T Rabczuk, X Zhuang. Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Advances in Engineering Software, 2018, 122 : 31– 49 https://doi.org/10.1016/j.advengsoft.2018.03.012
23
S Zhou, X Zhuang, T Rabczuk. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350 : 169– 198 https://doi.org/10.1016/j.cma.2019.03.001
24
S Zhou, X Zhuang, H Zhu, T Rabczuk. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96 : 174– 192 https://doi.org/10.1016/j.tafmec.2018.04.011
G Klee, F Rummel, A Williams. Hydraulic fracturing stress measurements in Hong Kong (China). International Journal of Rock Mechanics and Mining Sciences, 1999, 36( 6): 731– 741 https://doi.org/10.1016/S0148-9062(99)00036-4
27
A Ghanbari, S Shams Rad. Development of an empirical criterion for predicting the hydraulic fracturing in the core of earth dams. Acta Geotechnica, 2015, 10( 2): 243– 254 https://doi.org/10.1007/s11440-013-0263-2
28
A S Vesić. Expansion of cavities in infinite soil mass. Journal of the Soil Mechanics and Foundations Division, 1972, 98( 3): 265– 290 https://doi.org/10.1061/JSFEAQ.0001740
K H Andersen, C G Rawlings, T A Lunne, T H By. Estimation of hydraulic fracture pressure in clay. Canadian Geotechnical Journal, 1994, 31( 6): 817– 828 https://doi.org/10.1139/t94-099
31
Mitchell J K, Soga K. Fundamentals of Soil Behavior. New York: John Wiley & Sons, 2005
32
E Sarris, P Papanastasiou. Modeling of hydraulic fracturing in a poroelastic cohesive formation. International Journal of Geomechanics, 2012, 12( 2): 160– 167 https://doi.org/10.1061/(ASCE)GM.1943-5622.0000121
33
S Tang, Z Dong, J Wang, A Mahmood. A numerical study of fracture initiation under different loads during hydraulic fracturing. Journal of Central South University, 2020, 27( 12): 3875– 3887 https://doi.org/10.1007/s11771-020-4470-3
34
X N Wang, Q M Li, Y Z Yu, H Lu. Hydraulic fracturing simulation of soils based on XFEM. Journal of Geotechnical Engineering, 2020, 42( 2): 390– 397
35
X Zhuang, S Zhou, M Sheng, G Li. On the hydraulic fracturing in naturally-layered porous media using the phase field method. Engineering Geology, 2020, 266 : 105306– https://doi.org/10.1016/j.enggeo.2019.105306
36
P Q Mo, A M Marshall, H S Yu. Interpretation of cone penetration test data in layered soils using cavity expansion analysis. Journal of Geotechnical and Geoenvironmental Engineering, 2017, 143( 1): 04016084– https://doi.org/10.1061/(ASCE)GT.1943-5606.0001577
37
H Cheng, Z H Fu, G X Zhang, B Yang, C F Jiang. Reinforcement effect analysis and global safety evaluation of Wugachong arch dam and its abutment. Rock and Soil Mechanics, 2017, 38 : 374– 380
38
Wang L, Feng M, Zhang H. The tension fracture simulation on the asphalt pavement with the insufficient compaction roadbed. In: The 1st International Conference on Civil Engineering, Architecture and Building Materials, CEABM 2011. Haikou: Trans Tech Publications, 2011
39
S M Sayed, M A Hamed. Expansion of cavities in layered elastic system. International Journal for Numerical and Analytical Methods in Geomechanics, 1987, 11( 2): 203– 213 https://doi.org/10.1002/nag.1610110209
40
Yu H S. Cavity Expansion Methods in Geomechanics. Norwell: Springer Science & Business Media, 2000
H Ling, W Wang, F Wang, H Fu, H Q Han. Experimental study on hydraulic fracture of gravelly soil core. Journal of Geotechnical Engineering, 2018, 40( 8): 1444– 1448
43
Z Zhou, X Cai, D Ma, W Cao, L Chen, J Zhou. Effects of water content on fracture and mechanical behavior of sandstone with a low clay mineral content. Engineering Fracture Mechanics, 2018, 193 : 47– 65 https://doi.org/10.3901/JME.2018.12.193
44
X Sun, X Li, B Zheng, J He, T Mao. Study on the progressive fracturing in soil and rock mixture under uniaxial compression conditions by CT scanning. Engineering Geology, 2020, 279 : 105884– https://doi.org/10.1016/j.enggeo.2020.105884
45
G W Jaworski, J M Duncan, H B Seed. Laboratory study of hydraulic fracturing. Journal of the Geotechnical Engineering Division, 1981, 107( 6): 713– 732 https://doi.org/10.1061/AJGEB6.0001147
46
J J Wang, Y X Liu. Hydraulic fracturing in a cubic soil specimen. Soil Mechanics and Foundation Engineering, 2010, 47( 4): 136– 142 https://doi.org/10.1007/s11204-010-9101-9
47
L Bjerrum, J K T L Nash, R M Kennard, R E Gibson. Hydraulic fracturing in field permeability testing. Geotechnique, 1972, 22( 2): 319– 332 https://doi.org/10.1680/geot.1972.22.2.319
48
A Mori, M Tamura, Y Fukui. Laboratory studies on some factors related to fracturing pressure of cohesive soils. Soils and Foundations, 1991, 31( 1): 222– 229 https://doi.org/10.3208/sandf1972.31.222
